Claude Cibils
Professeur émérite
Institut Montpelliérain Alexander Grothendieck
IMAG  UMR5149

Université de Montpellier
CC 51
F-34095 Montpellier cedex 5
France

+33 467144831
egin_of_the_sky end_of_the_skype_highlightinClaude.Cibils *at* umontpellier.fr
 

Former director of CIMPA

   






  

 

Messages directeur I3M 2004-08
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GTA
Géométrie, Topologie et Algèbre.


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On the first τ-tilting Hochschild cohomology of an algebra

Claude Cibils, Marcelo Lanzilotta, Eduardo N. Marcos, Andrea Solotar

In this paper we introduce, according to one of the main ideas of τ-tilting theory, the τ-tilting Hochschild cohomology in degree one of a finite dimensional k-algebra Λ, where k is a field. We define the excess of Λ as the difference between the dimensions of the τ-tilting Hochschild cohomology in degree one and the dimension of the usual Hochschild cohomology in degree one.

One of the main results is that for a zero excess bound quiver algebra Λ=kQ/I, the Hochschild cohomology in degree two HH2(Λ) is isomorphic to the space of morphisms 𝖧𝗈𝗆kQkQ(I/I2,Λ). This may be useful to determine when HH2(Λ)=0 for these algebras.

We compute the excess for hereditary, radical square zero and monomial triangular algebras. For a bound quiver algebra Λ, a formula for the excess of Λ is obtained. We also give a criterion for Λ to be τ-rigid.

Ediiteur de Homology, Homotopy and Applications.


Thèses soutenues

2019 : Marco Antonio Armenta Armenta
2015 : Sergio Chouhy
2009 : Selene Sanchez
   2006 : Patrick Le Meur
2002 : Eric.Reynaud
2002 : Claudia Strametz
2001: Rachel Taillefer
2001 : Elisabet Gunnlaugsdottir